Sometimes people say thatgtpmd:4qe/, xs7ob2ozdl e, 8- d2 rpe water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wropge: 82 d m/dd4,oexr 2p-7 ebsz,qlotng with this statement?

Will the acceleration of a car be the same when the car05f)woc( k7gln,zoi q travels around a sharp curve noi(o 0)fz7 kg5clqw, at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly re* ja(hmjiyh)jd(*mitqxr4t q, 9x1. oad. Where does the car exert the greatest and least force h9mqhay*jjiidt1rx4(,qmje) t *( x .s on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. ;q(bx y4s2yghkrhkt 44x x9p5Which of these forces provides the centripetal acceleration ofyk4b xh;s 9x5r 24gqt pkyh(4x the child?

A bucket of water can be whirled in a vertical circle wit;brz1(jfqzw e5yxy3) hout the water spilling out, even at the5j xfbz)yw1 (;3zrqye top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Th.j 3uvhgw4yk5a 39usiere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelehij3 5w9uyv 3ags uk.4rations do they produce?

A child on a sled comes flying over the crest of a small m6m- ir zg)j- ng+8al z4d(yjae-o0 nihill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the8i geo4 (zlmi nr-g)0jad-6jna-m+z y hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at h9bi0rr *pc (owigh speed?

Why do airplanes bank when they tuft/ *dxv e.e-7j vyt ccu04dv8rn? How would you compute the banking angle given i8v.dvytdecu/ c t-fvx0e4 j* 7ts speed and radius of the turn?

A girl is whirling aeg3zqudd 4kj+x 8j m83 ball on a string around her head in a horizontal plane. She wants to let8de 8jd4jg3 kq3z+uxm go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how lagw yjcv ava:/08: ,6q lduoa-arge a force? Consider an ag0v 8aj :yu , odwcv-6a/qala:pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what :y10d;tj s -x2uvqesztyyd-s .7i vz3it is, in what ways would the Moon’s orbit be diffe0t2vz.vsu- t yyie:xs;z j-1d 7sdqy3 rent?

Which pulls harder gravitationally, the Earth on the M;4 c5 pu0dfzrajnd1 h:oon, or the Moon on the Earth? Which azfn1a c: 5jr0 hd4;udpccelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th vxgfvc6 8 akwi3vy(3;e Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the othervcxf6;k8i 3gy 3wvv( a.]

Will an object weigh more at+pyijzv;y-6g a s):nl the equator or at the poles? What two effects are at work? Do s+n6 ijaz; -l :)pvyygthey oppose each other?

The gravitational force)u 2px5qq7gkw -4t+ tt7dc sap on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’ttkpts-cx5 t7 q+a7g wdu24q)p the Moon pulled away from the Earth?

Is the centripetal acceleration of ccyciu l, f,(b)mlv6*Mars in its orbit around the Sun larger or smaller than the centripetal accel,,6cfm *b(l ucvi)cyleration of the Earth?

Would it require less speed to launch a satellite (a) towwhaiy z nqt:u x+t z(6efd9 331y(7onnard the east or (b) toward the west? Consider tuxwqt+n nd(z f6y7z3t ay 93ohni1e(:he Earth’s rotation direction.

When will your apparent weight be the g:c ,:0hr 2k+ dk(italc3xxds lreatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downwa0skixr2(l thdcd +k :xl,:c3ard, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods3li028 z1qcreuv rr9n in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotarrqzceurl23 09 8ni1vtes, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparentru3 5:ur 7dfp l)q/clr weightlessness” between st / pq 3rdrurfl5:)7culeps.

The Earth moves faster in its orbit aroun 54n0amvd;3 nzv4fjot;rz1tmd the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its odv 5zota1f3mn 4r; mt;j0 4znvrbit.]

The mass of Pluto was not known until it was discovf5,fs:xnc :av ,)grr3/po ,n9bflwmx ered to have a moon. Explain how this discovery enabled an estimate of Plut p:n) mox, fs/v xrbr,w5ffa,lg:n9c3o’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet22 (coy2 2z7tjpmtu9p3 4mhatz u0h qg the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difhuu2p 2m 4tajyc3o 0q927z 2zmt(thpgference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19 * ghq)sdt7vk ( xx;,b/fsx1vz80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around theav1sw4ba cr 21 Sun, and the net forc1r 1ba 2wcvas4e exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 p sxvlta858 ;oi,y:;t .eb6eystk zl 5N is exerted on a 2.0-kg discus as it rotates uniformly i5l i;6 sz;y,yvtka8 :bs .8elx5totepn a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sur d;y/q)f5l (am0qd2 so9uafwg face, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its or ;y f9uf)q a2lodw5dq/( 0asgmbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on thpok: g(xuyxoa d5)k 3*e edge of a potter’s wheel turning at 45 rpm (revolutions per minute) ifpau( k o53dxyk*g xo:) the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circlentaw9eidz )mz3x-h7p ; 6nv/zwi l;;3:n blbe of radius 72.0 cm , an); n/xmptdvle3l w znb;-:ba i 79we zi36h;zs shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum sdfo55j8x- to )r1am 4ywa3iq ww -dsz+peed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coeffic4-1f m8)dzwdi+say53- ortax5 qwojw ient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction bedfe znv6* f1qnz+3ac4 between the tires and the road if a car is to round a level curve of radius 85 m at aq1fv6zf3an +nc d4 ez* speed of 95km/h ?   

  A device for training astronauts a x;z7;bbo8 jej/ymbq7 nd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight,z;yjx q7mjb 7eob8/;b how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of vari 9j8, tqzwxte;able speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?t ,wjz9q x;et8   

  At what minimum speed must a rolleroh5b2u)05 xc pmedapw *kh q97 coaster be traveling when upside down at the top of a cir9bxck *)d2wea7muhqpo 5h0p5 cle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses(ev7 jqi cor,88r 8xvd the rounded top of 7ei o8qvrc 8,xrjv(d8a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel n)pit5 obh4m2 p20f,:tkw;b u agh*rvd eed to make for the passengers to fee p0dgtotb*b p2f;v: u)wi h, akr42hm5l “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of h bp/fzso+q,9 radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N./s z pf9,hoq+b
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a uj pc lf (p2 e-bwe.8ro2uky/7kk8hi+ particle 9.00 cm from the axis of rotation is to experience an acceleration ofhlr+youk( p/ ubk7-j 8k8.iewp f22ce 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated.m-bo9j)j wbsp,/ji,+i vkvb in a cylindrically walled "room.,p.ijjk)s o v-vbimwbb+/ 9,j" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circyzndn9 0zyc3u 5uda:zdr j74y1*c; k fpa8l, ble on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling bloc47uzan jzblnyu8z5c rdc : y0*1,yd dk3pa;f9k (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this t-1rj;h i7rz wxime, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude;zrwri- xjh71 of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius ofo y)v u ix oql04z/na:;//gnhf 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massekuexa iuc 86((s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertical(bmt0hd2 pt 3xly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net f0e qr ax4n m5wr,7 nju:bna;w,orce exerted on the car (by the ground) i0wrn;5,em 7na 4jqa:ur ,nbxwn Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianap9l vsgid( a(:oolis 500 accelerates uniformly from the pit area, going from rest:o9a(l ds( ivg to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circ7i rb1l w)*xoule of radius 2.90 m . At a particular instant, its accwoxl 71biu)*releration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force 1tadjk3y 7o, f;bg nowczh,s)z5( 0uxof Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) sfo3n,cgz0 5)y,;btuaow 7j (dh zx1kabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratief j5;zuf);dl52cwqa xppf*/l+yr u; on g has a magnitudl2)f;5crj dp;xfy5zl/w;u ep aq+u f*e of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moooewc 0;72hhli/h f e)on's radius is 1.70h 7/hwhfiolc e);2oe4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius (a kkq hjd;*ts8 itfo0/5m(9;jn gydd1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity nearqm;o dj8h0* (kkjytdd9 is5 g( ;ant/f its surface?   

  A hypothetical planet has a mass 1.66 times that of Eartk)ix:62js36 fi fkc gzh, but the same radius. What is g near its :)6fk i32fji cg 6skxzsurface?   

  Two objects attract each other gravitationally wil0gn h* 9oy) qe+o:fic5dj p+np /szc3th a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value ooagj4b m d/k1oeiv(39n0ff5xf g , the acceleration of gravity, at (a) 3200 m xfo eo 09d/mvb5fa(ijg 1kn34    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whe /yz:f6xdal g;re thegravitational acceleration due to the z;d:y/ agl6xf Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass bh mfa5r3k1+i m;er( w1w fm+xof our Sun packed into a sphere about 10 km in radius. Ea3 bfif+1km h;mxw( 5rme1w+rstimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likmnof,2- mabsieo( u7/e our Sun but is now in the last stage of its i en7-ubo /som2ma f(,evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting iab 20ocjkgg)9+/d zxgh7.p eox*g +ton the space shuttle. Your friends respon 9gpg.e+ 7 oc0)gahzd2xjx*oo /gbtk+d that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of zrw .ub) f/ec7a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othwf.czu /b e7r)er three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years m u/tm /.gkva7most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter,vgm k.tu7/m/a and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surwwnqz0+(q,r7 m5 g: :mvjtv q)obp5zvface of Mars is 0.38 of what it is on E z+: nvzqq o,j 0pg mqvb55):rmtw(vw7arth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of thex970:ph oaq ro Sun using the known value for the period of the Earth and its distance from the p7:hoox aq0r9 Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular 1,w h2k+me3+ bcmk99v rh 6iawkpx b::rd7ep worbit about the Earth at a height of 329d9:rxhpw3 r kekep17+ 6bmwwk h+mb: ic,va600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbu y5/txz ;tijnbwn)7 6qka5 (hit 650 km above the Ear 5ty ;u() 5 zhkqb6tnn7jx/iwath. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spac( l xwf2ma9.nceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the t92.la wmncf( xime needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a ci f4mm7av34z qvk:0pxnn .5odcrcular “near-Earth” orbit. A “near-Earth” orbit is one at a heq4cv7 o35xf:adk0mn.n 4m pvz ight above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to /ht0xhxay 3u1+b9 (mmrx2opybe launched from the top of Mt. Everest to be placed in a circular orm1a+/u(2 y9p0xt3xmby hr hoxbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued18p ml,:e6ld7c a 8gteidc xh7 to orbit the Moon at an altitude6:t m7ixd 7ce8 ,8 glpd1lchae of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that(-iwa 7:yx*yjil sj* oh0o;st orbit the planet. The inner radius of the rings is 73,s w-jyxh**7soyloti0a:;(ij 000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5ad k3bmh a:g+5–9). What is the ratiokm ah3b+ dg:a5 of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fror8 0lm8, wat))s eavqxm the center of the Earth's Moon ine08 )xal8a vm,) twqrs a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of rxtg/bq3+i-eqizcx(2yn )vy8;p 2 fy equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years 2ctpz;f+ 2yer)-nb3yv xyi/8q qgx(ito orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg / iw+y3w:rya6 b 2 cqgpt/-2yd9 lzgyfwoman in an elevator that mov69yy3 g/agip :wcwbq fl2/r zy-2+yt des
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspendejkq 5vk7 6vm7ky4u qis)p7;yqd from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was t75v4ky6 pu v)kqky;jsq qi7 7mhe elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite uz fxc;8zt8j id /o( 1wf a)jn8u5;qmqorbits very near the surface of a planet with period T , the density (mass/volume) z8(cjfx w;n/mt 8;aiq )8f ud5oz1juqof the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period b7g8uwfd1 s+fof an artificial sate+f8f1 usw 7gbdllite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a fe5o b mom,2 qkkad)-xbw-i-h0e2op3xkw hundred meters across, orbits the Sun like the planets. Its period is 410 d5 ax0kk- xomqbdoi2) , e b-kohwmp-32. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of lj8k ks;ac -t .8ga+tdp(6bmv4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun r hmt6vfc 2.v- 3 ux4fjugz*n)woughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and f.n3vmtf*wu-ch6) zu gv4j2x f arthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galax/ dm08bfao7dq -1bztly $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the massum yao)3yn(i* , period, and mean distance for the four largest moons of Jupiter (those discovered by Gal aum*n)3y(ioyileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distanh cx16pvnz,; 45bte ynce of the Moon. xeh ;pb 4n,z ty16cnv5   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s mooigye* gv0o+-36saxu tns, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the *0-yis6o 3uxave+tg gTable.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmen 1f,*upfj5 rv;7 ,tjs d:mgfvlts (which some space scientists think came from a planet that once orbited the Sun buvt:u ,m;vr ld1,f *gf5s7j jfpt was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in a3pw xdzjpa:kkj4,y;q2 51re the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the pryz 4xwj2k3k:j,q1ade 5pp a;eriod of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig8 wb rq ojna-az/jt-,+okj:r9. 5–41). If hib-9 j+zon-wrjk:,ta ar8qo/j s arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration ofys uv byq-skkl)8:p /+,mqer pga 3z73 gravity be half what it is o /s) pu3yq8bmr,ke-3+7vzsk : qgay lpn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutzhzgb(i+9.o n ual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, hhi.+o nzbzg( 9ow hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dm/- vp55jtpwuay, the apparent acceleration of gravity at the equator is slightly lessuv5m j- 5pw/tp than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft t-b udga d i)cwrq4u4-)raveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and uaqdg4 4r-bcu)di -)wopposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an e98*yyag vq pi1levator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whic v8yqyp1g*i9ah direction?     ----待选择----upwartddown 

  A projected space station consists of m: )fm5 s5adoie ; l1)7p*jdxmb d:sgwa circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutios*;m :w )xo75dpa die5mm:fl dg)sj b1ns per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). i(c. qej i0ocr78tk0w
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in te/t h.*ocy; vwj mb(y2jq,cr)orms of its radius r, the acceleration due to gravity at its surface and the gravitatioj/vooht . ;qmr cy wcy(2j,b*)nal constant G.

A plumb bob (a mass m hanginlax ,ik :bh 5c9n36ttjtv: yn6g on a string) is deflected from the vertical by aj5t9in ahtn:63:l 6vckt yx,bn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If thdib;; 3e x3bu(no0sdee coefficient of st(d xubde0n; 3 3si;eobatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that* h-+yiqgt4rm 9us52s nddw (q objects at the equator tsn4g-rqi9mqwh (*d+ysu5d 2 were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apa 8h;..)g v vzih*wy1jh-fxw irh+f8xtrt of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp moo yg+4wn1i +susmw1i nyo++4go pended from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive asbh hobei+x2+ o*u+7el the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a pers2+*ol7 i++xbehbou e hon would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremzfr- om4x x/9jely massive core in the distant galaxy M87, so dense that it could be a b jrmz49o/-fxxlack hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and va0x be 2c4wbd+ i-di0j(,ll;i rat5phalley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contacl-l40b ixpc(,art0 ddhwi5ae ; +bi2jt with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 sac :f9h00sk 5a;bkp9 xemsy d6ptellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at abpsmcy;a6h0p:9 kd9skf05 xen altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), eg ;c: qt d,+o2(,ampxgotoht 3/ty5cafter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 k,(t5/3eo+pto c2 g:g,tc ;axhdqy tmom . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttld7axni ))) r. pph,0psldd8 ake pursuing a satellite in need of repair. You are in a circular orbit of the s)8,ah ) xdr7paisd0ln. )p kpdame radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period oi*xr np 71 equ-sr tdl0.tdg qzo0s4,r;;l1g jf 3000 years. (a) What is its mean distance frosel; xzd1tdsu 7r 1i n0ot 4g*qrglrj.-,;qp0m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if 4xg)pm 4e7wf wyou could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions4eww7p)4g mx f, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cente vsht,+wa7w5au c53yl r of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from t5l+u7w, ty awv3 5sahche center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at th uozktfa9o 1gsa : 1vcg1sm-:0ov7f7q e corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kzk7s uvaq9:-7oga mof01g t f:scv11og mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thezp,azgvo zw)/ t0 (,cl Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the accelera4zu tp b1:27+:g9gihhgju wip tion experienced by the tip of the 1.5-cm-long sweep second b9:24gpuu th+h :j1zwi pgig7hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circ4ml o*cfj;oqm/xa + s;le below you on a 0.25-m piece of fishing line. qslm m4;+f;c o/jao* xThe weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new w q6/fea;lxj, highway is designed so that a car traveling at sqlew 6f/; jxa,peed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the car +j kml(hjx3eqn( sp3dm42(ml-e9n yvs when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate thp(+q xnvjm9- 3lh( 4ms3 n emye2jdkl(e friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$